The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the
most successful domain decomposition solvers for partial differential equations. The …

The adaptive BDDC method is extended to the selection of face constraints in three
dimensions. A new implementation of the BDDC method is presented based on a global …

We combine the adaptive and multilevel approaches to the BDDC and formulate a method
which allows an adaptive selection of constraints on each decomposition level. We also …

Recent advances in high performance computing systems and sensing technologies
motivate computational simulations with extremely high resolution models with capabilities …

The spectral stochastic finite element method (SSFEM) may offer an efficient alternative to
the traditional Monte Carlo simulations (MCS) for uncertainty quantification of large-scale …

The BDDC method [2] is one of the most advanced methods of iterative substructuring. In the
case of many substructures, solving the coarse problem exactly becomes a bottleneck …

In conjunction with modern high performance computing platforms, domain decom position
methods permit computational simulations of physical and engineering systems using …

We extend the balancing domain decomposition by constraints (BDDC) method to flows in
porous media discretised by mixed‐hybrid finite elements with combined mesh dimensions …

We study a framework that allows to solve the coarse problem in the FETI‐DP method
approximately. It is based on the saddle‐point formulation of the FETI‐DP system with a …